A178328 - OEIS

%I #22 Jun 26 2023 06:33:34

%S 2,21,121,211,223,631,1211,1663,1811,1831,2127,2813,4211,5497,6211,

%T 8411,12149,12287,18113,19121,23311,24113,24311,27311,31651,32129,

%U 32221,34171,38131,41213,47231,49183,53831,56831,111223,111421,111811,121279,123121,129151,141233,156271,157651,161171

%N Numbers k such that k^p-p is prime, where p is product of the digits of k.

%C 2 is the only even term of this sequence. Large numbers corresponding to some terms are probable prime.

%e 21^(2*1) - (2*1) is prime so 21 is in the sequence.

%t Do[p=Apply[Times, IntegerDigits[n]]; If[PrimeQ[n^p-p], Print[n]], {n, 54891}]

%t (* or *)

%t ppdQ[n_]:=Module[{p=Times@@IntegerDigits[n]},PrimeQ[n^p-p]]; Select[ Range[ 120000],ppdQ] (* _Harvey P. Dale_, Nov 12 2017 *)

%Y Cf. A007954, A178327.

%K base,nonn

%O 1,1

%A _Farideh Firoozbakht_, May 29 2010

%E a(34)-a(37) from _Max Alekseyev_, Feb 19 2012

%E a(38)-a(44) from _Michael S. Branicky_, Jun 25 2023